(x^2+4xy-5y^2)=0

Solution for (x^2+4xy-5y^2)=0 equation:

Simplifying
(x2 + 4xy + -5y2) = 0

Reorder the terms:
(4xy + x2 + -5y2) = 0

Remove parenthesis around (4xy + x2 + -5y2)
4xy + x2 + -5y2 = 0

Solving
4xy + x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(x + 5y) = 0

Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

Move all terms containing x to the left, all other terms to the right.

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Subproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.
x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
x + 0 = 0 + -5y
x = 0 + -5y
Remove the zero:
x = -5y

Simplifying
x = -5y
Solution
x = {y, -5y}